can you list the steps on how to solve this (how to get to the answer), please. ---### Calculus Problem: Related Rates**Problem Statement:**The length of a rectangle is increasing at a rate of $6 \, \text{cm/s}$ and its width is increasing at a rate of $3 \, \text{cm/s}$. When the length is $13 \, \text{cm}$ and the width is $9 \, \text{cm}$, how fast is the area of the rectangle increasing?\[ \text{Rate of increase of area} = \boxed{ \text{cm}^2/\text{s} } \]---**Explanation:**This problem involves related rates, a common type of problem in calculus where we determine how one quantity changes as another quantity changes. To solve this problem, you must understand how the dimensions of a geometric shape (in this case, a rectangle) relate to its area and how changes in these dimensions affect the area over time.1. **Identify Variables:** - Let $ l $ represent the length of the rectangle. - Let $ w $ represent the width of the rectangle. - Let $ A $ represent the area of the rectangle.2. **Given Rates:** - The rate of change of length $ \frac{dl}{dt} = 6 \, \text{cm/s} $ - The rate of change of width $ \frac{dw}{dt} = 3 \, \text{cm/s} $3. **Formula for the Area of Rectangle:** - The area of the rectangle is $ A = l \times w $4. **Differentiate with Respect to Time:** - Use the product rule to differentiate the area with respect to time. \[ \frac{dA}{dt} = \frac{d}{dt} (l \times w) = l \frac{dw}{dt} + w \frac{dl}{dt} \]5. **Substitute Given Values:** - Length $ l = 13 \, \text{cm} $ - Width $ w = 9 \, \text{cm} $ - Now plug in the values and the rates of change into the differentiated formula. \[ \frac{dA}{dt} = (13 \, \text{cm}) \times (3 \, \text{cm/s})

Answered: Image /qna-images/answer/b0049ffd-b143-4f42-8890-0d69fbb0ac8d.jpg

Answered: n you list the steps on how to s

n you list the steps on how to s

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

Similar questions

Tom is 4 more than twice Andrews age. Sarah is 8 less than 5 times Andrew ‘s age. If Tom and Sarah are twins, how old is Andrew?
A sausage machine produces 159 sausages per hour. The machine operates 365hours per month.How many sausages does it produce per month? Work the problem in the spacebelow and write the answer on the line below.
Please help solve it, thank you. Tim got his first paycheck from his new job, worked 25 hours, and earned $356.25. How much is earned per hour?
zaida ran 8/9 miles and anita ran 1 1/3 miles. How many more miles did anita run that zaida solve using a number line and explain your solution.
Please help me!
can you please solve the other o
Kindly solve question two please
Sarah walks 4 miles every evening. She is also a golfer. Since playing an average 18-hole golf course involves walking 6300 yards total (when the ball is hit straight), she wondered how many holes she walked the equivalent of every time she went for her evening walk. Find the equivalent number of holes Sarah walked each evening. For this problem you may round to the nearest whole number. (1 mile = 5280 feet.)
The word JOURNEY is written over and over again on a long strip of paper (without any blank spaces between words). What letter is the 1389th place counted from the beginning? how could I come up with an equation to solve this mathmatically?
Could you write out the solution or make it more clear. I can't read the work when it is a jumble of numbers. Thank you.